The strict requirements for process modeling, monitoring and control make online and accurate identification of key quality variables important in modern industry. However, in many industrial circumstances, it is extremely difficult to timely measure these key variables owing to reasons such as hostile site-on environment, high economy or analyzer cost, and large time delay. In order to overcome the shortcomings of traditional measurement technology, soft sensors, which are developed by modeling the regression relationship between output and input variables, have been widely used to predict the hard-to-measure quality variables through easy-to-measure process variables. As alternatives for hardware sensors, soft sensors have gained popularity because they are able to online measure the quality variables in a low cost and high efficiency way.
Generally speaking, soft sensor models fall into three categories, which are first-principle based, data-based, and hybrid models. Because of the high complexity of modern industrial processes, complete knowledge is difficult to obtain, which places restrictions on the use of first principle models, as well as the hybrid models. By contrast, data-based models can be conveniently built because a distributed control system can provide a vast volume of process data. Therefore, they have been more and more popular in both academia and industry. Many typical data-driven soft sensor approaches, including principal component regression, partial least squares, artificial neural network, support vector machine, and Gaussian process regression, have successful applications in industrial processes. The probabilistic density-based methods occupy an important position among them, because they consider the input and output variables as random variables and model them through probabilistic density or probabilistic distribution, which is a more reasonable way in handling noises and uncertainty issues compared with the deterministic methods.
It is important in a probabilistic distribution-based model to select a proper distribution to approximate a data structure. Among all probabilistic distributions, Gaussian is the most commonly used because of the central limit theory and its convenience for implementation. Although Gaussian achieves numerous successful applications, it may have some limitations when handling nonlinear and multimode characteristics along with a complex process mechanism, operating condition change, and feedstock switching.
Approaches dealing with nonlinearity and multimodality can be roughly categorized into two types: finite mixture model-based approaches and just in time learning (JITL)-based approaches. In the former, a training dataset is first partitioned into several sub-datasets via clustering methods such as k-means and Gaussian mixture model. Then the data samples falling into each sub-dataset are trained to build a sub-model, and the prediction results of each sub-model are combined to obtain the final prediction of quality variable. However, the finite mixture model-base approaches have some shortcomings in application. First, it is usually difficult to provide prior process information on the number of sub-datasets. Second, the prediction accuracy heavily depends on the result of clustering algorithms. Third, the computing burden and model complexity are huge especially when the number of sub-datasets is large.
In the JITL modeling framework, when a query sample is available, a local model is trained by using the most similar and relevant historical samples. Since the similar samples always share a homogeneous process mechanism, the local model can be more reasonable and accurate than the global model. Each local model is built uniquely and distinguished by the similarities between the query sample and each training sample, which makes JITL an effective tool in nonlinear and multimode process modeling. Its main advantage over a finite mixture model is that it relies on few underlying process knowledge. Thus it is more flexible and convenient in reality.
For a good visual presentation, FIGS. 10A-10C give a comparison of data description of a global model (FIG. 10A), finite mixture model (FIG. 10B), and JITL (FIG. 10C). The red line is the real function for data generation and the blue dots are samples collected in the historical dataset. The ellipses represent the estimated model of different methods. In particular, the left ellipse and right ellipse in FIG. 10C represent the estimated model around a query sample with a regular value, and a peak value, respectively.
Data-driven soft sensors are often based on complete data samples which contains both input and output variables. In practice, however, a vast number of training data samples are accessible while only a small portion of them are labeled, owing to the fact that output variables are often quality variables that are difficult to measure due to the highly expensive labeling cost of time, human efforts, and laboratory instruments. In traditional JITL models, only labeled data can be effectively utilized for local modeling, and a large number of unlabeled data samples are ignored and deleted. It is apparently inadvisable because without using unlabeled data samples, data information is not sufficiently exploited. Moreover, the developed soft sensor may not be guaranteed to provide reliable and accurate predictions, especially when the number of labeled data samples is quite small.
One exemplary application of soft sensors for industry is in fractionating columns. For instance, a debutanizer column is an important part of an industrial refinery and is used to split desulfuration and naphtha. The propane and butane in naphtha stream are removed through a debutanizer column process. For process safety and product quality the butane content in the debutanizer bottoms is desired to be minimized. For this purpose, its real-time measurement is of significance. However, it is difficult for traditional hardware sensors to timely measure the butane content, because gas chromatograph is not installed at the debutanizer bottom, but the overheads of the subsequent deisopentanizer column, which leads to a large measurement delay. A faster and more effective way of obtaining butane bottoms measurements is needed.